Here we employ PIP approach to fit both the \(V_{LL}\)  and \(\Delta {V_{CC-LL}}\)  PESs.
The theory of permutationally invariant polynomial is well established and has been presented in several review articles.[1]}, [2]}, [3]}, [4]}, [5]} In terms of a PIP basis, the potential energy, \(V\) , can be written in compact form as
\(V({x})= \sum _{i=1}^{n_p} c_i p_i({x}),\) 
